Roger Altman, Evercore executive chairman, says the threat of a government shutdown “is different this time because it involves a social policy issue—Planned Parenthood—instead of the typical fiscal and sequester issues.”

“It might be harder to resolve because of that," Altman told CNBC. "It's probably the case that there's going to be a shutdown," said Altman, a Treasury official in the Carter and Clinton administrations.

U.S. lawmakers have until the end of the month to finalize the country's budget, but are at odds over a bill that would provide funding for the nonprofit organization. Investigations are under way into two secretly recorded videos that appeared to show Planned Parenthood was involved in the illegal sale of aborted fetal tissue for medical research.

Altman said a short shutdown will not have a meaningful impact on the U.S. economy, "although, there's no guarantee of that."

Federal Reserve Chair Janet Yellen last week seemed to have a message for any lawmaker who's considering holding the budget hostage: Don't even think about it.

"We have a good recovery in place that's really making progress, and to see Congress take actions that would endanger that progress—I think that would be more than unfortunate," Yellen said at the conclusion of a two-day meeting on monetary policy.

While the threat of a shutdown played "absolutely no role" in the central bank's decision to delay an interest-rate increase, it could very well become a risk going forward, joining market turmoil, sluggish global growth and weak inflation as potential negatives to the U.S. economy, Bloomberg News reported.

Funding for the government expires on Sept. 30, and some Republicans are insisting that any bill they send to President Barack Obama should cut money for Planned Parenthood.

The women's healthcare provider been scrutinized since the release of undercover videos showing some staffers discussing reimbursement for fetal tissue they provide medical researchers.

“Republican leadership in both houses has begun this discussion by preemptively surrendering to Barack Obama and saying, 'We'll give in because Obama threatens a veto,'" Texas Senator Ted Cruz said at the Republican presidential debate in Simi Valley, California.

“We need to stop surrendering and start standing for our principles.”

If that stance led to a shutdown, what follows could be a replay of October 2013, the last time such an event occurred. Consumer confidenceplunged, economic reports were delayed and many Americans were temporarily thrown out of work.

That may be one reason Republican Ohio Governor John Kasich, who served in Congress and chaired the House Budget Committee, last night urged caution when it comes to shutdown rhetoric.

"All we're gonna do is shut the government down, and then we're gonna open it up, and the American people are gonna shake their heads and say, 'What's the story with these Republicans?'”